AT: Average treatment effect of a binary endogenous variable

Description

AT can be used to calculate the sample average treatment effect of a binary endogenous predictor/treatment, with corresponding confidence/credible intervals.

Usage

AT(x, eq, nm.bin = "", E = TRUE, treat = TRUE, delta = FALSE, 
   prob.lev = 0.05, s.meth = "svd", n.sim = 500, naive = FALSE)

Arguments

A fitted SemiParBIVProbit object as produced by SemiParBIVProbit().

Equation containing the binary endogenous predictor of interest.

nm.bin

Name of the binary endogenous variable.

If TRUE then AT calculates the sample ATE. If FALSE then it calculates the sample AT for the treated individuals only.

treat

If TRUE then AT calculates the AT using the treated only. If FALSE then it calculates the effect on the control group. This only makes sense if used jointly with E = FALSE.

delta

If TRUE then an approximate delta method is used for confidence interval calculation, otherwise Bayesian posterior simulation (the most reliable option, despite a bit slower) is employed. Note that for models inv

prob.lev

Probability of the left and right tails of the AT distribution used for interval calculations.

s.meth

Matrix decomposition used to determine the matrix root of the covariance matrix. This is used when delta = FALSE. See the documentation of the mvtnorm package for further details.

n.sim

Number of simulated coefficient vectors from the posterior distribution of the estimated model parameters. This is used when delta = FALSE. It may be increased if more precision is required.

naive

It indicates whether the AT is calculated from a univariate probit model. This option has been introduced to compare adjusted (for unobserved confounding) and unadjusted estimates. Note that, although the unadjusted estimates

Value

resIt returns three values: lower confidence interval limit, estimated AT and upper confidence interval limit.
prob.levProbability level used.
est.ATbIf delta = FALSE then it returns a vector containing simulated values of the average treatment effect. This is used to calculate intervals.

Details

AT measures the sample average difference in outcomes under treatment (the binary predictor or treatment assumes value 1) and under control (the binary treatment assumes value 0). Note that this function is only suitable for the calculation of the average treatment effect in recursive bivariate binary models. Posterior simulation and delta method can be used to obtain confidence/credible intervals. The former is typically more reliable at small sample sizes. See the references below for details.

References

Marra G. and Radice R. (2011), Estimation of a Semiparametric Recursive Bivariate Probit in the Presence of Endogeneity. Canadian Journal of Statistics, 39(2), 259-279. Radice R., Marra G. and M. Wojtys (submitted), Copula Regression Spline Models for Binary Outcomes.

Examples

Run this code

## see examples for SemiParBIVProbit

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